A quantitative study of the interactions between oil price and renewable energy sources stock prices

In this article, we apply an integrable nonautonomous Lotka-Volterra model to study the relationship between oil and renewable energy stock prices between 2006 and 2016. The advantage of this innovative approach is that it allows us to study the simultaneous interaction among n stock indices at any point in time. In line with previous studies, we find that the relationship between oil and renewables is characterized by major structural breaks taking place in 2008 and around 2013. The first structural break might be caused by the financial crisis, whereas more studies are required to advance a hypothesis on the causes behind the second structural break. Our main finding is that oil is always in a predator-prey relationship with wind, whereas it proceeds in mutualism with solar after 2012. Moreover, we find that solar and wind proceed in mutualism between 2008 and 2013 but have a rivalrous interaction before (competition) and after (predator-prey) that period. We explore the possible reasons behind these patterns and their policy implications

Dynamical system theory of periodically collapsing bubbles

We propose a reduced form set of two coupled continuous time equations linking the price of a representative asset and the price of a bond, the later quantifying the cost of borrowing. The feedbacks between asset prices and bonds are mediated by the dependence of their "fundamental values" on past asset prices and bond themselves. The obtained nonlinear self-referencing price dynamics can induce, in a completely objective deterministic way, the appearance of periodically exploding bubbles ending in crashes. Technically, the periodically explosive bubbles arise due to the proximity of two types of bifurcations as a function of the two key control parameters $b$ and $g$, which represent, respectively, the sensitivity of the fundamental asset price on past asset and bond prices and of the fundamental bond price on past asset prices. One is a Hopf bifurcation, when a stable focus transforms into an unstable focus and a limit cycle appears. The other is a rather unusual bifurcation, when a stable node and a saddle merge together and disappear, while an unstable focus survives and a limit cycle develops. The lines, where the periodic bubbles arise, are analogous to the critical lines of phase transitions in statistical physics. The amplitude of bubbles and waiting times between them respectively diverge with the critical exponents $\gamma = 1$ and $\nu = 1/2$, as the critical lines are approached.Comment: Latex file, 35 pages, 16 figure

A Three Class Predator-Prey Model with Financial Super Predators: The Financial Profit Squeeze

The primary purpose of this paper is to: 1) introduce a three-class predator-prey model with class interactions consistent with the NL era into the literature; 2) analyze the spectrum of different qualitative macroeconomic behaviors associated with the model; 3) focus on two particular outcomes – FK PS and a double reserve army (RA) – FK PS –both capable of producing cyclical and chaotic outcomes; and 4) use the FK PS to explain key stylized facts associated with the NL period. Given a sparing behavioral structure for the model where financial markets are not explicitly specified3, a full-on calibration exercise is not attempted

Extreme events in population dynamics with functional carrying capacity

A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations between populations can be realized not merely through direct interactions, as in the usual predator-prey Lotka-Volterra model, but also through the influence of species on the carrying capacities of each other. This includes the self-influence of each kind of species on its own carrying capacity with delays. Several examples of such evolution equations with functional carrying capacities are analyzed. The emphasis is given on the conditions under which the solutions to the equations display extreme events, such as finite-time death and finite-time singularity. Any destructive action of populations, whether on their own carrying capacity or on the carrying capacities of co-existing species, can lead to the instability of the whole population that is revealed in the form of the appearance of extreme events, finite-time extinctions or booms followed by crashe

Innovation, imitation and policy inaction

The paper deals with the controversial issue of intellectual property rights. We deal with an optimization problem to model the optimal government's behavior in presence of dynamic uncertainty and intervention costs. More specifically, we search for the optimal strategies to be implemented by a policy maker to optimally balance the number of innovators and imitators. The problem is first tackled from a purely theoretical perspective and then by implementing extensive numerical simulations on the basis of empirical data. By the theoretical perspective, we obtain a rigorous proof that optimal strategies depend on the initial value of the number of imitators and not on the initial ratio between innovators and imitators, whereas the simulations provide us with intuitive insights from an economic point of view, along with a validation of the theoretical results. The results support the evidence that governments choose the possible widest bandwidth and minimize the size of interventions so as to curb intervention costs

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Three Essays in Economics of Prey-Predator Relation

This dissertation explores how natural ecosystem can be integrated with economic system through two case studies of multiple species interactions, or predator-prey relations. By the inclusion of biological, ecological and economic aspects, the integrated approaches aim at more clearly understanding of how regional ecosystem and economy interact with each other, given threats of resource extinction and environmental shock. I also explain strategies and policy regimes that can be considered to achieve efficient and sustainable ecosystem management in those circumstances. The first case study focuses on a predator-prey relation in the Pacific Ocean between the United States and Canada, where endangered/threatened predators feed primarily on commercially valuable species as prey. Accounting for the importance of those predators as critical natural resources for whale watching industry, this case study synthesizes the species biological and the regional economic systems, and analyzes possible management strategies for both ecosystem conservation and sustainable economic growth. A long-term drought and fragmented management has been one of the critical issues in the Great Salt Lake (GSL) ecosystem that is linked with its regional economy in Utah. For this issue, the second case study builds an integrated model for describing how the lakes main natural resources, such as water, brine shrimp, and migratory birds, are related to primary industries in the region including agriculture, mining, fishery, and recreation. With the model framework, the study presents how the prolonged drought affects both the GSL ecosystem and its rigional economy, and suggests economic management strategies for the lakes ecosystem recovery in the presence of drought

Using emergent order to shape a space society

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems

Modeling economies and ecosystems in general equilibrium

This work exploits the general equilibrium modeling framework to simulate complex systems, an economy and an ecosystem. In an economic application, this work leverages a novel data revision scheme to integrate technological detail on electricity generation and pollution abatement into national accounts data in a traditional economic computed general equilibrium (CGE) model. This integration provides a rich characterization of generation and abatement for multiple fuel sources and pollutants across 72 different generation-abatement technology configurations. Results reveal that the benefits of reductions in oxides of nitrogen and sulfur from a carbon policy in the US electric sector are on the order of $10 bn., which rival the policy's welfare costs and make 12-13% carbon abatement economically justifiable without considering any climate benefits. For ecosystem applications, this work demonstrates how the structure of economic CGE modeling can be adapted to construct a Biological General Equilibrium (BGE) model grounded in the theoretical biology literature. The BGE model contributes a novel synthesis of micro-behavioral, bioenergetic features with macroscopic ecosystem outcomes and empirical food web data. Species respond to prevailing ecosystem scarcity conditions that impinge on their energy budgets driving population outcomes within and across model periods. This adaptive capacity is a critical advance over the commonly-taken phenomenological or first-order parametric approaches. The distinctive design of the BGE model enables numerical examination of how changes in scarcity drives biomass production and consumption in a complex food web. Moreover, the BGE model design can exploit empirical datasets used by extant ecosystem models to offer this level of insight for a wide cast of ecosystems. Monte carlo simulations demonstrate that the BGE framework can produce stable results for the ecosystem robust to a variety of shocks and parameterizations. The BGE model's validity is supported in tests against real-world phenomena within the Aleutian ecosystem - both an invasive species and a harvesting-induced trophic cascade - by mimicking key features of these phenomena. The BGE model's micro-founded dynamics, the stability and robustness of its results, and its validity against real-world phenomena offer a unique and valuable contribution to ecosystem modeling and a way forward for the integrated assessment of human-ecosystem interactions